Undirected Cross Connects Based on Wavelength-Selective Switches

ABSTRACT

Undirected cross connects are provided based on wavelength-selective switches A demand d={i, j} is routed over a path p d  between ports i and j in a multi-layer network based on one or more wavelength selective switches, by determining a middle layer node n in the multi-network for which there is a first path p i  between the port i and the middle layer node n and a second path p i  between the port j and the middle layer node n; identifying a node n′, wherein the node n′ is a first node starting from port i that path p i  shares with path p j ; and concatenating the path p d  comprised of a subpath p i ′ of the first path p i  from the port i to the node n′ with a subpath of p′ j  of the second path p i  from the node n′ to the port j. An undirected Cantor network is disclosed where the switch nodes are wavelength selective switches. An undirected Clos cross connect is also disclosed where one or more undirected switches are undirected Cantor networks having at least one wavelength selective switch

FIELD OF THE INVENTION

The present invention relates to wavelength-selective switches, and moreparticularly, to undirected cross connects employing suchwavelength-selective switches

BACKGROUND OF THE INVENTION

The nonblocking of cross connect switches in a communications networkassesses the ability to route connections from input ports to outputports A cross connect C can be thought of as a directed graph whereinput ports are nodes with no incoming edges and output ports are nodeswith no outgoing edges A request for a connection from an input port ato an output port b will be a request for a directed path from a to bFor a more detailed discussion of nonblocking cross connects, see, forexample, J. Y. Hui, Switching and Traffic Theory for IntegratedBroadband Networks, Kluwer Academic Publishers, Norwell, Mass. (1990)and G. M. Masson et al, “A Sampler of Circuit Switching Networks,” IEEEComputer, 5:32-48 (June 1979)

For many networks, however, such as long-haul optical networks,connection requests have “bidirectional symmetry” In other words, thereis a request to connect i to j if and only if there is also a request toconnect j to i and moreover these two connections should be routed onthe same bidirectional links. See, J Simmons et al, “OpticalCrossconnects of Reduced Complexity for WDM Networks with BidirectionalSymmetry, IEEE Photonics Technology Letters, 10(6):819-821 (June 1998).This is due to the fact that optical network management is typicallydesigned to connect transceivers in pairs A restriction to bidirectionaldemands may allow for simplified cross connect designs For bidirectionaldemands, a cross connect will not have input and output ports, insteadit will just have ports

The cross connect will be an undirected network where the ports are leafnodes and a request for a connection will be a request for an undirectedpath between two ports. This is of interest when one has symmetricdemands (i.e., there is a demand d from node i to node j if and only ifthere is a demand d′ from node j to node i) and moreover demands d andd′ should be routed along the same undirected path

A cross connect is said to be strictly nonblocking if all connectionsfrom input ports to output ports can be routed without disturbing otherconnections A cross connect is said to be widesense nonblocking if thereexists a routing algorithm such that if all previous connections havebeen routed using that algorithm, then that algorithm will find a routefor any subsequent connection requests

A need exists for a modification to traditional cross connect designsfor this undirected case A further need exists for improved crossconnect designs for the undirected case that exhibit good nonblockingproperties. Yet another need exists for improved cross connect designsbased on various four-port switches

SUMMARY OF THE INVENTION

Generally, undirected cross connects are provided based onwavelength-selective switches According to one aspect of the invention,a method is provided for routing a demand d={i, j} over a path p_(d)between ports i and j in a multi-layer network based on one or morewavelength selective switches. The method comprises the steps ofdetermining a middle layer node n in the multi-network for which thereis a first path p_(i) between the port i and the middle layer node n anda second path p_(j) between the port j and the middle layer node n;identifying a node n′, wherein the node n′ is a first node starting fromport i that path p_(i) shares with path p_(j); and concatenating thepath p_(d), comprised of a subpath p_(i)′ of the first path p_(i) fromthe port i to the node n′ with a subpath of p′_(j) of the second pathp_(j) from the node n′ to the port j A demand routed in accordance withthe disclosed method can be considered widesense non-blocking

According to another aspect of the invention, an undirected Cantornetwork is disclosed that comprises k ports; at least one layer ofswitch nodes, wherein the switch nodes are wavelength selectiveswitches; and k switches for connecting the k ports to the at least onelayer of switch nodes The k switches can be, for example, 1×3 switchesIn one exemplary embodiment, the disclosed undirected Cantor networkcomprises half of a directed version of a Cantor network The disclosedundirected Cantor network can be simplified by replacing one of morenodes in a middle layer by one or more connections and then merging aspairs one or more nodes in a final layer that are connected by twoparallel links

According to yet another aspect of the invention, an undirected Closcross connect is disclosed that comprises k ports; n first stage p×mswitches connected to the k ports; and a plurality of second stageundirected switches, wherein one or more of the undirected switches areundirected Cantor networks having at least one switch node that is awavelength selective switch The first stage switches can be hybrid crossconnects

A more complete understanding of the present invention, as well asfurther features and advantages of the present invention, will beobtained by reference to the following detailed description and drawings

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 2 illustrate exemplary reflective wavelength selectiveswitches that can be used in accordance with the present invention toconstruct an undirected cross connect;

FIG. 3 illustrates an exemplary 8×8 Cantor network;

FIG. 4 illustrates an alternative exemplary 8×8 Cantor network;

FIG. 5 illustrates an exemplary 8×8 undirected Cantor network inaccordance with an embodiment of the present invention;

FIG. 6 is a flow chart describing an exemplary implementation of arouting algorithm, Alg, incorporating features of the present invention;

FIGS. 7 and 8 illustrate simplified versions of the exemplary 8×8undirected Cantor network of FIG. 5;

FIG. 9 illustrates a conventional Clos cross connect design having kinput ports and k output ports;

FIG. 10 illustrates an undirected Clos Cross network with k ports, inaccordance with the present invention; and

FIG. 11 illustrates an exemplary implementation of a 2×3 Clos crossconnect switch.

DETAILED DESCRIPTION

The present invention provides undirected (or bidirectional) widesensenonblocking cross connects based on four-port switches.

Directed Cross Connect Definitions

A k×k directed cross connect is a directed graph C with k source nodes(i.e, nodes with no incoming edges) called input nodes and k sink nodes(i.e., nodes with no outgoing edges) called output nodes. A directeddemand is a request for a directed path in C from an input node to someoutput node The notation d=(i, j) denotes the directed demand d withinput node i and output node i. A set S of directed demands is valid ifall directed demands in S have distinct input nodes and distinct outputnodes. A routing R_(d) of a directed demand d is a directed path in Cfrom the input node to the output node of d A valid Touting of a validset of directed demands S is a set of routings R={R_(d): dεS} so that ifd, d′εS, then R_(d) and R_(d) are are disjoint.

Undirected (or Bidirectional) Cross Connects Definitions

A size k (undirected) cross connect C is an undirected graph with k leafnodes called ports. A demand is a request for a path in C between a pairof ports. The notation d−{i, j} denotes the demand d that requires apath between ports i and j A set S of demands is valid if no two demandsin S have a port in common. A routing R_(d) of a demand d is a path in Cbetween the ports of d A valid routing of a valid set of demands S is aset of routings R−{R_(d)εS} so that if d,d′εS, then R_(d) and R_(d) areedge disjoint

Hybrid Cross Connects

A hybrid cross connect is an undirected (bidirectional) network that hastwo sets of ports A and B A hybrid demand is a request for a pathbetween a pair of ports in A or a request for a path between a port in Aand a port in B

General Definitions

All definitions in this section are given for undirected cross connectsbut remain the same for directed (or hybrid) cross connects if the term“demand” is replaced by “directed demand” (or “hybrid demand”)

There are traditionally three levels of′ nonblocking from strongest toweakest, they ate:

-   1. Strictly Nonblocking—A cross connect is strictly nonblocking if    for all valid demand sets S, all valid routings R of S, and any    demand d∉S such that S′=S∪{d} is a valid demand set, there is a    valid touting R′ of S′ such that R⊂R′.-   2. Widesense Nonblocking—A cross connect is widesense nonblocking if    there is a routing algorithm, Alg, such that for all valid demand    sets S, all valid routings R of S that have been computed using    algorithm Alg, and any demand d∉S such that S′∉S∪{d} is a valid    demand set, algorithm A/g will find a valid routing R′ of S′ such    that R⊂R′.-   3. Rearrangeably Nonblocking—A cross connect is rearrangeably    nonblocking if for any valid set of demands S there is a valid    touting R of S

Wavelength Selective Switches

Although the present invention is illustrated herein in the context ofoptical networks and in particular, wavelength division multiplexing(WDM) networks, the disclosed cross connects are not specific to anyparticular kind of network e g., optical, electronic or wireless meshnetworks, as would be apparent to a person of ordinary skill in the art

The cross connects will be wavelength selective cross connects In otherwords, each demand will be a request to route a particular wavelengthbetween two given ports

U.S. patent application Ser. No. 11/434,938, entitled, “Multiple PortSymmetric Reflective Wavelength-Selective Mesh Node,” filed May 16, 2006(Attorney Docket No Doerr 116-27), and incorporated by reference herein,discloses reflective wavelength selective switches (WSS) used asbuilding blocks for the undirected cross connects disclosed herein Seealso, U.S. patent application Ser. No 11/434,919, entitled, “MultiplePort Symmetric Transmissive Wavelength-Selective Mesh Node,” filed May16, 2006 (Attorney Docket No Doerr 117-28), incorporated by referenceherein

Generally, the disclosed reflective wavelength selective switchesmultiplex and demultiplex the wavelengths at each port and there is asteering mirror for each available wavelength. The switches are designedso that they are nonblocking, i e., a connection made by the switch doesnot have to be interrupted when it is subsequently required to form anadditional connection

FIGS. 1 and 2 illustrate reflective wavelength selective switches 100,200 that can be used in accordance with the present invention toconstruct an undirected cross connect In FIGS. 1 and 2, the switches100, 200 have an open circle to indicate each port and have solid dotsto indicate mirror states independently chosen for each wavelength

Degree-4 Node

The exemplary 1×6 WSS switch 100 shown in FIG. 1 is an undirected crossconnect with four ports for providing one channel of a multiplewavelength channel signal with reciprocal connectivity between nodeports A, B, C, and D. For a four port mesh node, a total of4!/[2!(4−2)!] or 6 unique node port pair connections must be made by the1×6 WSS apparatus. Note that only terminal 4 (of the seven terminalslabeled left to light as 0-6) of the 1×6 WSS switch 100 is unconnectedTwo of the terminals (2 and 5) are directly connected to node ports Band D, respectively The node port A connects via a 1×2 directionalcoupler (not shown) to terminals 1 and 3 of the 1×6 WSS apparatus 100The node port C connects via a 1×2 directional coupler (not shown) toterminals 0 and 6. The steerable mirror of the 1×6 WSS is switched toone of three positions (or states), as denoted by the left, center, andright connection dots “•”. The 1×6 WSS 100 is switchably controlled by acontrol signal (not shown) to enable reciprocal connections to beestablished between six unique pairs of node ports (i.e., AB, AC, AD,BC, BD, BC) by switching the minor, to one of the three positions Thus,as shown in table 110, in a first switching state (1) (associated withleft connection dot), two simultaneous connections are made betweenports A-B and C-D (since two sets of terminals 2 and 3 as well as 0 and5 are symmetrically located around the left connection dot). In thesecond switching state (2) (associated with the center connection dot),a connection is made between ports A-C and B-D (since the terminals 1and 6 as well as 2 and 5 are symmetrically located around the centerconnection dot) In the third switching state (3) (associated with thetight connection dot), a connection is made between ports A-D and C-B(since the terminals 3 and 5 as well as 2 and 6 are symmetricallylocated around the right connection dot) In this manner, a reciprocalconnection is established between each unique pair of node ports byswitching the mirror of the 1×6 WSS to one of the three positions Whilethe degree-4 mesh node has been shown to include a 1×6 WSS, it should benoted that any 1×K switch can be used, where A′ is greater than or equalto 6, with the additional terminals left unconnected

Partitioned Degree-4 Node

The exemplary 1×6 WSS switch 200 shown in FIG. 2 is an undirected crossconnect with four ports for providing one channel of a multiplewavelength channel signal with reciprocal connectivity between nodeports A, B, C, and D FIG. 2 illustrates a hybrid design, referred to asa hybrid-4 node with six terminals As shown in table 210, the switch 200can connect port A with port B or alternatively can connect port A withport C and port B with port D or port A with port D and port B with portC

Note that only terminal 3 (of the six terminals labeled left to right as0-5) of the 1×5 WSS switch 200 is unconnected Three of the terminals (1,4 and 5) are directly connected to node ports B, D and C, respectivelyThe node port A connects via a 1×2 directional coupler (not shown) toterminals 0 and 2 of the 1×5 WSS apparatus 200 The steerable mirror ofthe 1×5 WSS is switched to one of three positions (or states), asdenoted by the left, center, and right connection dots “•”.

Along these same lines, a 3-port switch can be constructed that allowsonly the connection A-B or the connection A-C, as would be apparent to aperson of ordinary skill in the art. This will be called a 1×2 switch Ina straightforward manner, a 1×n switch can be constructed using n−1 such1×2 switches Also, one could implement a 1×n switch using a single n+1port WSS in a bidirectional way, as would be apparent to a person ofordinary skill in the art

The Cantor Network

The present invention recognizes that a traditional directed crossconnect can be modified to provide an undirected cross connect.

Directed Cantor Network

One well-known strictly nonblocking directed cross connect design is theCantor network See, D. Cantor; “On Construction of Nonblocking SwitchingNetworks,” Proc of Symp on Computer-Communications Networks andTeletraffic, 253-255 (1972) The structure of a k×k Cantor network can beviewed as follows In the middle of the network are log₂k copies of k×kBen{hacek over (e)}s networks. See, V. E Ben{hacek over (e)}s,Mathematical Theory of Connecting Networks and Telephone Traffic.Academic Press, New York, N.Y. (1935). The i^(th) input (output) node ofthe Cantor network is connected to the i^(th) input (output) node ofeach of the log₂k copies of the center Ben{hacek over (e)}s networks.

FIG. 3 illustrates an 8×8 Cantor network 300 As shown in FIG. 3, solidnodes on the left denote input nodes 310-1 through 310-8, solid nodes onthe right denote output nodes 320-1 through 320-8 and solid nodes inbetween represent the input and output nodes of the constituentBen{hacek over (e)}s networks The open circles are 2×2 switches,referred to as switch nodes The triangles are 1×3 switches 330-1 through330-8 and 340-1 through 340-8 All edges are directed from left to right.

Let C(k) be a k×k Cantor network made up of Ben {hacek over (e)}snetworks B₁(k), B₂(k), . . . , B_(m)(k), where m=log₂ k The switch nodesin all the B_(i)(k)'s can be thought of as being in layers (or columnsin FIG. 3 ) numbered from left to right starting at 0. Then, there are2log₂k−1 such layers with k/2 nodes in each layer. The notation L(v)denotes the number of the layer in which v lies The B_(i)(k) as well asC(k) are symmetric about the middle layer of the Ben{hacek over (e)}snetworks, that is about the log₂k−1 layer This middle layer has a totalof (k/2)log₂k nodes It is well-known that C(k) is strictly nonblockingSee, for example, G M Masson et al, “A Sampler of Circuit SwitchingNetworks,” IEEE Computer; 5:32-48 (June 1979).

FIG. 4 illustrates an alternative 8×8 Cantor network 400 FIG. 4 showsmore deafly the expansion aspects of the design that is used in theanalysis As shown in FIG. 4, solid nodes on the left denote input nodes410-1 through 410-8, solid nodes on the right denote output nodes 420-1through 420-8 The open circles are 2×2 switches, referred to as switchnodes The triangles are 1×3 switches 430-1 through 430-8 and 440-1through 440-8 The numbers 0, 1, 2 in FIG. 4 indicate the level numbersup to the middle level (level 2) To show that C(k) is strictlynonblocking, suppose S is a valid set of demands, B is a valid routingof S and S∪{d} is also a valid set of demands Then, it is desired toshow that there is a routing of the demand d=(i, j) that uses no edgesof the routes already used by R The notation A(m) is used to mean thelower bound on the number of nodes at the m^(th) layer to which there isa path from input node i that does not use any edges used by R It iseasy to see that A(0)=log₂k and inductively:

$\begin{matrix}\begin{matrix}{{A(m)} = {{2{A\left( {m - 1} \right)}} - 2^{m - 1}}} \\{= {{2^{m}{A(0)}} - {m\; 2^{m - 1}}}}\end{matrix} & \begin{matrix}(1) \\(2)\end{matrix}\end{matrix}$

This can be seen by noticing in FIG. 4 that the number of nodes that canbe reached at level m from input node i is twice the number that can bereached at level m−1 (since the out-degree of each node is two and theedges from the nodes in A(m) all go to distinct nodes at level m+1)Also, 2 ^(m−1) of the nodes that are reachable from input node i atlevel m+1 if no other demands are routed might in fact be blocked bydemands that have been routed. Then, at the middle layer

$\begin{matrix}\begin{matrix}{{A\left( {{\log_{2}k} - 1} \right)} = {\frac{k\; \log_{2}k}{2} - \frac{\left( {{\log_{2}k} - 1} \right)k}{4}}} \\{= \frac{k\left( \; {{\log_{2}k} + 1} \right)}{4}}\end{matrix} & \begin{matrix}\begin{matrix}(3) \\\;\end{matrix} \\(4)\end{matrix}\end{matrix}$

It can also be shown that there are at least the same number of nodes atthe middle layer from which there is a path to output node j Thus, thetotal of both of these lower bounds is

$\frac{k\left( \; {{\log_{2}k} + 1} \right)}{2}$

and this is greater than the total number

$\frac{k\; \log_{2}k}{2}$

of nodes in the middle layer (level 2). This implies that there must beat least one node n in the middle layer for which there is a path from ito n and a path from n to j such that no edge of either path is used byany path in R That is, there is a valid path for the demand d=(i, j).

It should be noted that the above argument actually shows the followingsomewhat stronger result Let A be a subset of the input nodes and foraεA let p_(a) be a path from input node a to some node b at some levelm_(a) where m_(a)>log₂k−1 Suppose i, j∉A Then, there are paths p_(i) andp_(j) starting at i and j respectively, and both ending at the same nodeat level log₂k−1 so that neither p_(i) not p_(j) shares any edge withany path p_(a), where aεA. (Note that p_(i) and p_(j) might have edgesin common) This can be used to show that a modified version of theCantor network in accordance with the present invention is widesensenonblocking

Undirected Cantor Network

The present invention considers widesense nonblocking cross connectsrather than strictly nonblocking cross connects Consider the Cantornetwork 300, 400 of FIGS. 3 and 4. In the directed case, there is aunique directed path from any input node to any given node in the middlelayer and similarly from any middle layer node to any given output nodeThus, the only real choice is which middle layer node a demand should berouted through Once that middle layer node has been chosen, the path isunique However, in the undirected case, there are paths from an inputnode to a middle layer node that could move back and forth and use upmost of the edges in the graph Thus, allowing arbitrary routings tendsto be much more difficult in the undirected setting

FIG. 5 illustrates an exemplary 8×8 undirected Cantor network 500 inaccordance with an embodiment of the present invention, where the numberof leaf nodes 510-1 through 510-8 is A=8 The open circles are 2×2switches, referred to as switch nodes The triangles are 1×3 switches Ingeneral, the construction is just the half of a directed version of aCantor network 400 from the input nodes 510 to the middle layer nodes520-1 through 520-12 (level 2). The middle layer nodes 520 are markedwith dashed circles in FIG. 5 The input or output nodes of the Cantornetwork 500 and those of the constituent Ben{hacek over (e)}s networksare not shown The undirected Cantor network 500 is widesense nonblockingfor symmetric demands

FIG. 6 is a flow chart describing an exemplary implementation of arouting algorithm 600, Alg, incorporating features of the presentinvention. Suppose S is a valid set of demands where P is a validrouting of S as computed by Alg Let d−{i, j} be a demand such that S∪{d}is valid (step 610) Find a middle layer node n during step 620 such thatthere is a path p_(i) between i and n and a path p_(j) between j and nwhere p_(i) and p_(i) share no edges of the routes of P Also, Alg isrestricted during step 630 so that p_(i) (and p_(j)) so that the layernumber of nodes increases as the path moves along p_(i) (and p_(i)) fromi (and j) to n. During step 640, n′ is the first node starting from ithat path p_(i) shares with path p_(j) Then, during step 650, thesubpath p′_(i) of p from i to n′ is concatenated with the subpath ofp′_(j) of p_(j) from n′ to j. This path is p_(d) It can be shown that anundirected Cantor network is widesense nonblocking using algorithm Alg

The route chosen for the demand {i, j} by Alg consists of edge disjointpaths from i and j to some common node along p_(i) and p_(j) This commonnode might be n or it might be some node at some lower level. Thus, C(k)is widesense nonblocking.

FIGS. 7 and 8 illustrate simplified versions 700, 800 of the 8×8undirected Cantor network 500 of FIG. 5 The open circles are 2×2switches, referred to as switch nodes. The triangles are 1×3 switches.It should be noted that the middle level nodes of FIG. 5 ate not reallynecessary since they are degree two That is, the middle level nodes canbe replaced with simple connections 720, as shown in FIG. 7 Then, the 12nodes at the final layer 730 in FIG. 7 that are connected by twoparallel links can be merged as pairs into six degree-4 nodes 830, asshown in FIG. 8 The complexity of the undirected Cantor network 500,700, 800 can be viewed as follows Each initial triangle node is a1×log₂k switch which can be constructed from a single 1+log₂k WSS asmentioned above The design of′ degree-4 nodes can be used in each of thenodes in the final stage of the undirected Cantor network. The othernodes in the design can each be realized using a single hybrid-4 node asdescribed above There are k log₂k such nodes in each of log₂k−2 levelsand k log₂k/2 at the final level. Thus, the total complexity of thedisclosed undirected Cantor networks is roughly k log₂ ²k

Clos Cross Connect

Consider a design based on a traditional directed strictly nonblockingClos cross connect

Directed Clos Cross Connect

FIG. 9 illustrates a conventional (3-stage) Clos cross connect design900 for k input ports 910-1 through 910-k and k output ports 920-1through 920-k Again, the actual graph is considered to be a directedgraph with edges directed from left to right It is well-known that if m,the number of center stage switches 915 is at least 2 p−1, then thedirected Clos cross connect is strictly nonblocking

Undirected Clos Cross Connect

As with the Cantor network, the present invention recognizes that awidesense nonblocking undirected cross connect can be constructed with kports based on the Clos design. FIG. 10 illustrates an undirected ClosCross network 1000 with k ports, in accordance with the presentinvention This general design has been investigated in early work thatwas interested in determining the minimum number of second stageswitches for a rearrangeably nonblocking design See, for example, WKabacinski, “Comment: Two-stage Non-Blocking Bidirectional SwitchNetworks,” Electronics Letters, 25(17):1198 (August 1989) and P Raby andP Banks, “Two-Stage Nonblocking Bidirectional Switch Networks,”Electronics Letters, 24(6):362-363, March 1988. However, they onlyallowed demands between ports on different first stage switches whereasthe present invention allows such demands plus demands where both portsare on the same first stage switch.

The k ports are connected to n first stage p×m switches 1010 The secondstage undirected switches 1020 with n ports can be implemented using,for example, the undirected Cantor network 500, 700, 800 described aboveThus, it is assumed that the second stage switches 1020 are allwidesense nonblocking

The first stage switches 1010 ale hybrid cross connects. That is, if Ais the set of p ports on the left side and B is the set of m ports onthe right side, then any set of demands must be supported where demandshave either both end ports in A or one in A and one in B Given that thesecond stage switches 1020 are widesense nonblocking, then if the hybridcross connects at the first stage 1010 are strictly or widesensenonblocking and m≧2 p−1 then the resulting undirected Clos Cross connectwill be widesense nonblocking

If p=2 and m=3, then a first stage switch 1010 can be built, asindicated in FIG. 11 FIG. 11 illustrates an exemplary implementation ofa 2×3 switch 1100 As shown in FIG. 11, the black circles 1130 indicateoptical couplers (i e, power combiner/splitters) and the rectangles1110, 1120 represent 5-port WSSs using the notation described above.Thus, the total complexity of the k/2 first stage switches 1110, 1120would be k/2 If undirected k/2×k/2 Cantor cross connects were used forthe three second stage switches 1130, each with roughly k log₂ ²k/2complexity, then the total complexity would be on the order of 3 k log₂²/2.

System and Article of Manufacture Details

As is known in the art, the methods and apparatus discussed herein maybe distributed as an article of manufacture that itself comprises acomputer readable medium having computer readable code means embodiedthereon The computer readable program code means is operable, inconjunction with a computer system, to carry out all or some of thesteps to perform the methods or create the apparatuses discussed hereinThe computer readable medium may be a recordable medium (e g, floppydisks, hard drives, compact disks, memory cards, semiconductor devices,chips, application specific integrated circuits (ASICs)) or may be atransmission medium (e.g, a network comprising fiber-optics, theworld-wide web, cables, or a wireless channel using time-divisionmultiple access, code-division multiple access, or other radio-frequencychannel) Any medium known or developed that can store informationsuitable for use with a computer system may be used Thecomputer-readable code means is any mechanism for allowing a computer toread instructions and data, such as magnetic variations on a magneticmedia of height variations on the surface of a compact disk.

The computer systems and servers described herein each contain a memorythat will configure associated processors to implement the methods,steps, and functions disclosed herein The memories could be distributedor local and the processors could be distributed or singular Thememories could be implemented as an electrical, magnetic or opticalmemory, or any combination of these or other types of storage devicesMoreover, the term “memory” should be construed broadly enough toencompass any information able to be read from or written to an addressin the addressable space accessed by an associated processor With thisdefinition, information on a network is still within a memory becausethe associated processor can retrieve the information from the network

It is to be understood that the embodiments and variations shown anddescribed herein are merely illustrative of the principles of thisinvention and that various modifications may be implemented by thoseskilled in the art without departing from the scope and spirit of theinvention

1. A method for touting a demand d={i, j} over a path p_(d) betweenports i and j in a multi-layer network having one or more wavelengthselective switches, said method comprising the steps of: determining amiddle layer node n in said multi-network for which there is a firstpath p_(i) between said port i and said middle layer node n and a secondpath p_(j) between said port j and said middle layer node n; identifyinga node n′, wherein said node n′ is a first node starting from port ithat path p_(i) shares with path p_(j); and concatenating said pathp_(d), comprised of a subpath p′_(i) of said first path p_(i) from saidport i to said node n′ with a subpath of p′_(i) of said second pathp_(j) from said node n′ to said port j.
 2. The method of claim 1,wherein said first and second paths p_(i) and p_(j) share no edges of aroute.
 3. The method of claim 1, wherein a layer number of nodesincreases along said first path p_(i) from said port i to said node n 4.The method of claim 1, wherein a layer number of nodes increases alongsaid second path p_(j) from said port j to said node n
 5. The method ofclaim 1, wherein a demand touted in accordance with said method iswidesense non-blocking.
 6. An undirected Cantor network, comprising: kports; at least one layer of switch nodes, wherein said switch nodes arewavelength selective switches; and k switches for connecting said kports to said at least one layer of switch nodes
 7. The undirectedCantor network of claim 6, wherein said k switches are 1×3 switches. 8.The undirected Cantor network of claim 6, wherein said undirected Cantornetwork comprises half of a directed version of a Cantor network
 9. Theundirected Cantor network of claim 6, wherein one or more nodes in amiddle layer are replaced by one or more connections.
 10. The undirectedCantor network of claim 9, wherein one or more nodes in a final layerthat are connected by two parallel links ate merged as pairs intodegree-4 nodes
 11. The undirected Cantor network of claim 6, whereinsaid wavelength selective switches comprise node port connection meansfor providing reciprocal connectivity between each of N node ports andterminals of a wavelength selective switch, so that each switch stateactivated by a control signal provides a set of at least one unique nodeport-pair connections
 12. The undirected Cantor network of claim 6,wherein said undirected Cantor network is widesense non-blocking
 13. Anundirected Clos cross connect, comprising: k ports; n first stage p×mswitches connected to said k ports; and a plurality of second stageundirected switches, wherein one or more of said undirected switches areundirected Cantor networks having at least one switch node that is awavelength selective switch
 14. The undirected Clos cross connect ofclaim 13, wherein said first stage switches ate hybrid cross connects.15. The undirected Clos cross connect of claim 13, wherein saidwavelength selective switch comprises node port connection means forproviding reciprocal connectivity between each of N node ports andterminals of said wavelength selective switch, so that each switch stateactivated by a control signal provides a set of at least one unique nodeport-pair connections
 16. The undirected Clos cross connect of claim 13,wherein said undirected Clos cross connect is widesense non-blocking 17.An apparatus for routing a demand d={i, j} over a path p_(d) betweenports i and j in a multi-layer network having one or mote wavelengthselective switches, the apparatus comprising: a memory; and at least oneprocessor, coupled to the memory, operative to: determining a middlelayer node n in said multi-network for which there is a first path p_(i)between said port i and said middle layer node n and a second path p_(j)between said port j and said middle layer node n; identifying a node n′,wherein said node n′ is a first node starting from port i that pathp_(j) shares with path p_(j); and concatenating said path p_(d)comprised of a subpath p_(i) ′ of said first path p_(i) from said port ito said node n′ with a subpath of p_(j)′ of said second path p_(j) fromsaid node n′ to said port j
 18. The apparatus of claim 17, wherein saidfirst and second paths p_(i) and p_(j) share no edges of a route
 19. Theapparatus of claim 17, wherein a layer number of nodes increases alongsaid first path p_(i) from said port i to said node n.
 20. The apparatusof claim 17, wherein a layer number of nodes increases along said secondpath p_(j) from said port j to said node n
 21. An undirected crossconnect node comprised of at least a first stage of directedwavelength-selective elements and at least one additional stage ofundirected wavelength-selective switch elements.